Question
A firm has tractors of four models A, B, C and D. Four tractors (two of model B and one each of models C and D) plough a field in 2 days. Two model A tractors and one model C tractor take 3 days to do this job. Three tractors one each of models A, B and C take 4 days to do the same task. How long will it take to do the job if a team is made up of four tractors of different models?
Answer: Option D
:
D
Method 1:
2B+1C+1D=12.............(i)
2A+1C=13...................(ii)
And 1A+1B+1C=14..........(iii)
On subtracting (i) and (ii) we get,
2A−2B−1D=16...................(iv)
On subtracting (iii) from (ii) we get
1A−1B=112
Therefore ,1B=1A−112.................(v)
From (ii), 1C=13−2A.......................(vi)
Using (i), (v) and (vi), we get
1D=12−2(1A−112)−(13−2A)=13
Therefore, 1A+1B+1C+1D=14+13=712
Hence time taken to complete the job =127 days.
Method 2:Using percentage approach (Recommanded)
Given that
2B+C+D=50 ............(1)
2A+C=33.33.............(2)
A+B+C=25...............(3)
(3)×2−(2)
2B+C=16.66
Substituting in (1)
D=33.33%
From (3) and adding D to it we get
A+B+C+D=68.88%=127 days.
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:
D
Method 1:
2B+1C+1D=12.............(i)
2A+1C=13...................(ii)
And 1A+1B+1C=14..........(iii)
On subtracting (i) and (ii) we get,
2A−2B−1D=16...................(iv)
On subtracting (iii) from (ii) we get
1A−1B=112
Therefore ,1B=1A−112.................(v)
From (ii), 1C=13−2A.......................(vi)
Using (i), (v) and (vi), we get
1D=12−2(1A−112)−(13−2A)=13
Therefore, 1A+1B+1C+1D=14+13=712
Hence time taken to complete the job =127 days.
Method 2:Using percentage approach (Recommanded)
Given that
2B+C+D=50 ............(1)
2A+C=33.33.............(2)
A+B+C=25...............(3)
(3)×2−(2)
2B+C=16.66
Substituting in (1)
D=33.33%
From (3) and adding D to it we get
A+B+C+D=68.88%=127 days.
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